Snell's law

Snell's Law is a formula used in Physics to describe the relationship between the angles of incidence and refraction, when referring to light or other waves passing through a boundary between two different isotropic media, such as water, glass, or air.

History

The law is named after the Dutch astronomer Willebrord Snellius (1580–1626), but was first accurately described by the Persian scientist Ibn Sahl in 984. The law follows from the principle of least time, which in turn follows from the principle of relativity.

Mathematical Formulation

In its simplest form, Snell's Law states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equivalent to the ratio of the velocity of light in the original medium to the velocity of light in the refracting medium. This can be written as:

n1 * sin(θ1) = n2 * sin(θ2)

where:

• n1 and n2 are the refractive indices of the first and second media respectively,
• θ1 is the angle between the incident ray and the surface normal (the line perpendicular to the surface at the point of incidence),
• θ2 is the angle between the refracted ray and the surface normal.

Applications

Snell's Law is used in many areas of physics, including in fiber optics, underwater diving, and optics. It is also essential in the design of lenses and prisms.

See Also

• Total internal reflection
• Critical angle
• Refractive index
• Fermat's Principle

References

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Snell's law

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  Diagram illustrating Snell's law

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  Ibn Sahl's manuscript on optics

• Snell Law of Sines 1837.png

  Snell's Law of Sines from 1837

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  Huygens' principle showing refracted waves

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  Portrait of Willebrord Snellius

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  Animation of Snell's law with wavefronts

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  Vector diagram of Snell's law

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  Diagram of refraction and internal reflection

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  Illustration of refraction and reflection